Paper Reading AI Learner

ODE Analysis of Stochastic Gradient Methods with Optimism and Anchoring for Minimax Problems and GANs

2019-05-26 23:05:13
Ernest K. Ryu, Kun Yuan, Wotao Yin

Abstract

Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate convergence of simultaneous gradient descent (simGD) and its variants under the assumption of convex-concavity, guided by a continuous-time analysis with differential equations. First, we show that simGD, as is, converges with stochastic sub-gradients under strict convexity in the primal variable. Second, we generalize optimistic simGD to accommodate an optimism rate separate from the learning rate and show its convergence with full gradients. Finally, we present anchored simGD, a new method, and show convergence with stochastic subgradients.

Abstract (translated)

尽管在经验上取得了显著的成功,但对于生成性对抗网络(gan)的训练动力学(gan)仍然知之甚少,它涉及使用随机梯度求解极大极小博弈。本文以微分方程连续时间分析为指导,在凸凹度假设下,分析了同时梯度下降(simgd)及其变化的最后一次迭代收敛性。首先,我们证明了simgd在原始变量的严格凸性下与随机次梯度收敛。其次,我们将乐观simgd推广到一个与学习率分离的乐观率,并显示其在全梯度下的收敛性。最后,我们提出了一种新的锚定simgd方法,并给出了随机子梯度的收敛性。

URL

https://arxiv.org/abs/1905.10899

PDF

https://arxiv.org/pdf/1905.10899.pdf


Tags
3D Action Action_Localization Action_Recognition Activity Adversarial Agent Attention Autonomous Bert Boundary_Detection Caption Chat Classification CNN Compressive_Sensing Contour Contrastive_Learning Deep_Learning Denoising Detection Dialog Diffusion Drone Dynamic_Memory_Network Edge_Detection Embedding Embodied Emotion Enhancement Face Face_Detection Face_Recognition Facial_Landmark Few-Shot Gait_Recognition GAN Gaze_Estimation Gesture Gradient_Descent Handwriting Human_Parsing Image_Caption Image_Classification Image_Compression Image_Enhancement Image_Generation Image_Matting Image_Retrieval Inference Inpainting Intelligent_Chip Knowledge Knowledge_Graph Language_Model Matching Medical Memory_Networks Multi_Modal Multi_Task NAS NMT Object_Detection Object_Tracking OCR Ontology Optical_Character Optical_Flow Optimization Person_Re-identification Point_Cloud Portrait_Generation Pose Pose_Estimation Prediction QA Quantitative Quantitative_Finance Quantization Re-identification Recognition Recommendation Reconstruction Regularization Reinforcement_Learning Relation Relation_Extraction Represenation Represenation_Learning Restoration Review RNN Salient Scene_Classification Scene_Generation Scene_Parsing Scene_Text Segmentation Self-Supervised Semantic_Instance_Segmentation Semantic_Segmentation Semi_Global Semi_Supervised Sence_graph Sentiment Sentiment_Classification Sketch SLAM Sparse Speech Speech_Recognition Style_Transfer Summarization Super_Resolution Surveillance Survey Text_Classification Text_Generation Tracking Transfer_Learning Transformer Unsupervised Video_Caption Video_Classification Video_Indexing Video_Prediction Video_Retrieval Visual_Relation VQA Weakly_Supervised Zero-Shot